Existence results for fractional <i>p</i>-Laplacian
problems via Morse theory

Iannizzotto, Antonio; Liu, Shibo; Perera, Kanishka; Squassina, Marco

doi:10.1515/acv-2014-0024

Cited by 198 publications

(153 citation statements)

References 41 publications

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“…The principal value definition (1.3) has been used in [17] to obtain regularity results in the context of viscosity solutions. Also, for general existence results and other regularity issues, we refer to the very recent contributions in [15], and in [2], where the related fractional p-eigenvalue problem has been considered.…”

Section: Introductionmentioning

confidence: 99%

Local behavior of fractional p-minimizers

Castro

Kuusi

Palatucci

2016

Ann. Inst. H. Poincaré C Anal. Non Linéaire

319

366

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Section: Introductionmentioning

confidence: 99%

Local behavior of fractional p-minimizers

Castro

Kuusi

Palatucci

2016

Ann. Inst. H. Poincaré C Anal. Non Linéaire

319

366

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“…In this section, following [10,18,30,32], we are going to prove Theorem 1.2 for (P λ ), when G is allowed to be possibly negative locally at 0 in the resonance case, but requiring that the weight a is in L ∞ (Ω). Again the (weak) solutions of (P λ )…”

Section: Proof Of Theorem 12mentioning

confidence: 99%

“…Lemma 4.1 is of independent interest and its argument relies somehow on previous strategies of [18,30], but with significant changes and improvements. Again the long proof of Theorem 1.2 is divided in a series of preliminary results given in Lemmas 3.1, 3.4, 3.7, and 4.1-4.4, as well as on some abstract results of the appendix which are useful to prove the main existence theorems.…”

Section: Introductionmentioning

confidence: 99%

Existence theorems for fractional p-Laplacian problems

Piersanti

Pucci

2016

Anal. Appl.

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The paper focuses on the existence of nontrivial solutions of a nonlinear eigenvalue perturbed problem depending on a real parameter λ under homogeneous boundary conditions in bounded domains with Lipschitz boundary. The problem involves a weighted fractional p-Laplacian operator. Denoting by (λ k ) k a sequence of eigenvalues obtained via mini-max methods and linking structures we prove the existence of (weak) solutions both when there exists k ∈ N such that λ = λ k and when λ / ∈ (λ k ) k . The paper is divided into two parts: in the first part existence results are determined when the perturbation is the derivative of a globally positive function whereas, in the second part, the case when the perturbation is the derivative of a function that could be either locally positive or locally negative at 0 is taken into account. In the latter case, it is necessary to extend the main results reported in [A. Iannizzotto, S. Liu, K. Perera and M. Squassina, Existence results for fractional p-Laplacian problems via Morse theory, Adv. Calc. Var. 9(2) (2016) 101-125]. In both cases, the existence of solutions is achieved via linking methods.

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“…Some existence and multiplicity results for fractional p-Laplacian problems, obtained through critical point theory and Morse theory, can be found in [22]. Nevertheless, the methods used in the present paper cannot be easily extended to (−∆) s p due to the lack of a complete boundary regularity theory like that developed in [33] for (−∆) s (some results in this direction are proved in [24]).…”

Section: Introductionmentioning

confidence: 96%